Rewrite as a simplified fraction. ${1.8\overline{4} = {?}}$
Answer: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 184.4444...\\ 10x &= 18.4444...\end{align*}}$ Subtracting the two equations, we have: ${90x = 166}$ ${x = \dfrac{166}{90}} $ ${x = \dfrac{83}{45}} \text{or} {1 \dfrac{38}{45}}$